Karman{40 s vortices generating device

ABSTRACT

A vortex generating element of the type used in flow metering apparatus and having a generally elongate cylindrical shape mounted in a stream of flowing fluid so as to produce Karman&#39;&#39;s vortices at a rate proportional to the velocity of the flowing fluid, with means detecting the production of vortices to give a linearly related measure of fluid velocity. To improve the correspondence of vortex production rate with flow velocity over wide conditions of flow, the element is formed on opposite sides thereof with recessed surface portions meeting the upstream surface of the element in an edge which lies substantially where the boundary layer of the fluid separates from the element surface during low velocity conditions of flow. The recessed surface portion meets the downstream surface of the element inwardly of said edge, whereby said edge forms an outer extremity of said element to said fluid flow and compels boundary layer separation.

United States Paten Yamasaki et al.

[451 Sept. 26, 1972 KARMAN 'S VORTICES GENERATING DEVICE inventors:Hiroo Yamasaki; Yoshio Kurita; Yu-

taka lshikawa; Takehiro Sawayama, all of Tokyo, Japan Yokogawa ElectricWorkds, Ltd., Tokyo, Japan Filed: April 23, 1971 Appl. No.: 136,980

Assignee:

Foreign Application Priority Data May 9, 1970 Japan ..45/3960l US. Cl...73/194 B Int. Cl....; ..G01f 1/00 Field of Search ..73/194 B, 194 CReferences Cited UNITED STATES PATENTS 1/1964 Bird ..73/194//j///////////)'/////////I i777 Primary Examiner-Richard C. QueisserAssistant Examiner-Herbert Goldstein Attorney-Bryan, Parmelee, Johnsonand Bollinger [5 7] ABSTRACT portions meeting the upstream surface ofthe element in an edge which lies substantially where the boundary layerof the fluid separates from the element surface during low velocityconditions of flow. The recessed surface portion meets the downstreamsurface of the element inwardly of said edge, whereby said edge forms anouterextremity of said element to said fluid flow and compels boundarylayer separation.

18 Claims, 12 Drawing Figures 24 VI I2A PULSE DEM PATENTEDSEPZB m2 SHEET1 BF 2 FIG.

FIG. 2

FIG. 3

DEM

L PULSE 12B EN Yuiaim [s/zZ/(awa BY Takekmo ,Sawayama A WWW 1 KARMAN 'SVORTICES GENERATING DEVICE BACKGROUND OF THE INVENTION 1. Field of theInvention This invention relates to flow metering apparatus of the typewherein a cylindrical object in a stream of flowing fluid produces awake including a distinct pattern of vortices known as the Karman VortexStreet. The vortices are shed from alternate sides of the object in aperiodic manner. There is a definite-relationship between frequency f ofshedding of the vortices, the diameter D of the cylinder, and thevelocity V of the stream, expressed by:

- f- -K'V/D where K is a constant when flow is within a range ofvelocities V, and where K is a function of velocity V outside thisrange. Accordingly, it is possible to determine the flow velocity V bymeasuring the frequency f of the generation of vortices, and themeasurement is straightforward where the conditions of flow make K aconstant.

' 2. DESCRIPTION OF THE PRIOR ART It has been found that the desiredlinear relationship between flow velocity V and frequency f of thevortex generation does not apply over the full range of conditionsencountered in flow measurement. When a cylinder is immersed in a streamof fluid flowing through a pipe and particularly when flow velocityincreases beyond a certain point, K is not a constant and themeasurement of vortex production does not simply yield a measurement ofvelocity. Though the causes of this disparity may not have yet beencompletely explained, it is believed to result from the uneven velocitydistribution of a fluid flowing through a pipe, from the fluctuation andeddies other than Karmans vortices which develop in the flowing fluid,and from the transfer to the downstream side of the cylindrical objectof the separating point of the boundary layer of the fluid flowing alongthe cylindrical surface as the flow velocity increases.

Various arrangements have been proposed for generating Karrnans vorticesmore stably in a flow measurement environment. In one such arrangementdisclosed in U.S. Pat. No. 3,564,915 Miyaji Tomota et al., thecylindrical element is formed with a transverse bore or slotintercepting the cylinder surface in the regions where boundary layerseparation occurs, with fluid flow alternating through the transversebore or slot as the Karmans vortices are generated and assisting incausing or retarding boundary layer separation for more reliable vortexproduction without influence from eddies and other fluid fluctuations.

In another prior art arrangement, disclosed in U.S. Pat. No. 3,116,639to Bird, the cylindrical object is formed with a cross-sectional shapewhich reduces flow resistance at high speeds, and avoids deleteriouseffects on vortex production caused by cavitation, such shapes includinga streamlined fore-part (such as a semi-ellipse) with the after part cutaway and recessed.

Such prior art apparatus of the general type referred to above has notbeen fully satisfactory in providing a linear relationship between flowvelocity V and the frequency f of vortex generation. While gains havebeen made in avoiding eddy and cavitation problems, deviations fromlinearity at high velocities of flow remain present.

. SUMMARY OF THE INVENTION It is a principal object of this invention toprovide improved elements for generating Karmans vortices, the frequencyof shedding of which is to be detected to measure the velocity of fluidflow. It is a specific object of the invention to provide a vortexgenerating element which extends the range of flow velocity for which alinear relationship exists between flow velocity and frequency of vortexgeneration. Still another object of the invention is to provide a vortexgenerating element of the type described which is more suitable forcommercial use.

In a preferred embodiment of the invention to be described hereinbelowin detail, the cylindrical element inserted in the flowing stream isformed on opposing sides with recessed surface portions. These portionsmeet the upstream portion of the element surface in an edge which liessubstantially where the boundary layer of the fluid separates from thesurface of the element at fluid velocities in the linear range. Therecessed surface portions also meet the downstream portion of theelement surface inwardly of said edge, and the edge thus forms an outerdiscontinuous extremity of the element to said fluid flow to forceboundary layer separation. This arrangement affords linearity ofoperation extending over a broader velocity range. The-arrangementfurther is advantageous in that it can employ a transverse borearrangement to further assist in controlling boundary layer separationto produce stable Karmans vortices.

Other objects, aspects and advantages of the invention will be pointedout in, or apparent from, the detailed description hereinbelow,considered together with the following drawings.

DESCRIPTION OF THE DRAWINGS FIG. I is a diagramatic illustration of theconventional mode of formation of Karmans vortices and of theirdetection in flow measuring apparatus;

FIG. 2 is a vertical longitudinal section through a fluid flow pipe,showing one form of the improved vortex generating element in elevation;

FIG. 3 is a cross section taken along line 3-3 of FIG.

FIGS. 4, 5, and 6 are cross-sectional views like FIG. 3 showing modifiedversions of the vortex generating element;

FIG. 7 is a view similar to FIG. 2 showing a portion of a modified formof a cylindrical element;

FIG. 8 is a view similar to FIG. 7 showing another modified form ofcylindrical element;

FIG. 9 is a cross section taken along line 9-9 of FIG.

FIG. 10 is a cross-sectional view similar to FIG. 9

. showing another modified fonn of vortex generating element;

FIG. 11 is a section on line 11 of FIG. 10; and

FIG. 12 is a view similar to FIG. 11 showing another modified form ofthe vortex generating element.

DESCRIPTION OF THE PREFERRED EMBODIMENTS that the fluid F breaks intotwo streams F1 and F2 at the stagnation point P1 and these two streamsflow along the surface of cylinder C. The flow velocity at the cylindersurface increases as the flow moves away from the stagnation point P1,until the boundary layer of the fluid separates from the cylindersurface at a separating point P2. Downstream of the separating point P2vortices form alternately on opposite sides of cylinder C to produce thecharacteristic Karman vortex street.

The separating point P2 of the boundary layer is not fixed, butperiodically varies its position along the circumference of cylinder Cas the alternating vortices are produced, oscillating about an averageposition which is stationary for a given flow velocity. The averageposition of separating point P2 also varies its position with flowvelocity. When the flow velocity is low, the average separating point P2is typically located on the upstream surface of cylinder C and isgradually transferred to the downstream surface as the velocityincreases. During the flow conditions which produce vortices, it hasbeen found that the position of the separating point P2 is located at anangle within a range of 75 to 105, where 0 is the angle between thecylinder radius connecting to the point P2 and the cylinder radiusconnecting to the stagnation point P1.

Variation of the angle 0 with velocity can also be put in terms of theReynolds number R=VD/V,, where V is the flow velocity, D is the cylinderdiameter, and V,, is the kinematic viscosity of the fluid. When theReynolds number is less than 10 the average position of separating pointP2 is located with the range of 0 of 75 to 85, and when the Reynoldsnumber exceeds as fluid velocity increases, the separating point P2 istransferred to the downstream side of the cylinder where 0 is greaterthan 90. At the lower Reynolds number, the frequency of vortexproduction is substantially linearly related to flow velocity.

The alternately shed vortices from cylinder C travel downstream of thecylinder, where the frequency of their production can be detected by adetecting means 12 positioned to intercept the vortices. The detectingmeans 12 can be a known arrangement comprising an electrically-heatablewire the ends of which are connected to a sensing circuit outside pipe10 which produces a flow of electric current through the wire and alsomeasures the change in resistance of the wire resulting fromdisplacement of the fluid accompanying the passage of vortices past thewire.

As indicated previously, when flow velocities are high, the conventionalcylinder illustrated in FIG. 1 does not provide the desired linearrelationship between frequency of vortex generation and flow velocity.Referring now to FIGS. 2 and 3 the present invention provides animproved vortex generating element 14, typically secured in place byattachment to the wall of pipe 10 as shown in FIG. 2. The shape ofvortex generating element 14 is generally elongate and cylindrical, butin a region L located centrally in pipe 10, the element 14 has providedthereon on opposite sides a pair of recessed surface portions 16, 18 asshown in cross section in FIG. 3.

The recessed surface portions 16, 18 are formed so as to intersect theupstream surface l4u of element 14 in discontinuities or edges 20, 22which are located substantially where the boundary layer of the fluidseparates from a cylindrical surface under conditions of low fluidvelocity which result in the linear relationship between vortexfrequency and flow velocity. As shown in FIG. 3, for example, edges 20and 22 are located at an angle 0 of approximately to The recessedsurface portions are also formed so that they meet the downstreamsurface 14d of element 14 in locations 24, 26 which are inward of edges20, 22, i.e., closer to the plane Pc extending through the cylinder axisand the stagnation point P1, which plane is also the plane of symmetryof the element 14. Thus the edges 20, 22 form the outer extremities ofelement 14 to the flow of fluid F, which as before breaks into twostreams, F1 and F2 as it impinges upon element 14. The streams F1 and F2flow along the upstream surface l4u until they reach edges 20, 22 wherethe boundary layer of the fluid separates from the elements surfacebecause of the existence of recesses 16, 18. The surface discontinuityprovided by the recesses 16, 18 provides for positive separation of theboundary layer with a concomitant positive and stable generation ofKarmans vortices, even at high flow velocities. The element 14 withrecesses 16, 18 formed thereon will generate Karmans vortices in astable manner, largely free of the influences of flow fluctuation andeddy currents in the stream, and will maintain a linear relationshipbetween the frequency of vortex generation and flow velocity over abroad range of flow velocities.

The cross-sectional shape of recesses l6, 18 may vary. In the embodimentshown in FIG. 3, the recesses 16, 18 are formed with two flat, planarsurfaces, the

. rear one parallel to the direction of flow F, and the front oneperpendicular to that direction and forming sharp edges 20, 22. Variousmodifications of the shape of recesses 16, 18 are shown in FIGS. 4through 6. In the embodiment of FIG. 4, element 14 has recesses 16a, 18aformed of a single flat surface along a chord of the cylinder. In theembodiment of FIG. 5, the element 14 has recesses 16b, 18b formed withcurved surfaces which undercut the edges 20, 22. In the embodiment shownin FIG. 6, there is shown an element 14c having an elliptical shape withmajor axis D1 and minor axis D2, the direction of flow being parallel tothe major axis. Recesses 16c, are formed with two flat, planar surfaces,the rear one parallel to the direction of flow and the front oneperpendicular to the direction of flow similar to the embodiment of FIG.3. The upstream edges 20 and 22 of the recesses 16c, 18c are locatedsubstantially where the boundary layer of the fluid flow separates atlow fluid velocities from the surface of an elliptical cylinder withaxes D1 and D2.

Detection of vortices generated by the element 14 can be by use of adetecting means 12 as shown in FIG. 1, or alternatively by use ofdetecting means 12a shown in FIG. 3. This detecting means is mounteddirectly on the downstream surface 14d of element 14 and comprises anelectrically heated wire sensing the displacement of fluid flowing alongthe downstream surface, the fluid flow having a variation directlyrelated to the production of Karmans vortices.

Still another detecting means 12b is shown in FIG. 3. (For simplicity,detecting means 12a and 12b are shown in superimposed use in FIG. 3, butthey would typically be used independently of one another.) Thedetecting means 12b detects the passage of Karmans vortices by makinguse of the vortex property of oppositely directed velocity components v1and v2 produced in the fluid F. Detecting means 12b comprises asupersonic pulse generator 30 feeding a transmitter 32 which sends thesound impulses across pipe to a receiver 34. Receiver 34 is connected toan input of the pulse generator 30, which is arranged to emit a newpulse each time one is received from receiver 34. Receiver 34 is alsoconnected to a frequency demodulator 36 whose output is fed to a counteror calculator 38. In operation, detecting means 12b transmits pulsesfrom transmitter 32 to receiver 34; the time required for thetransmission will depend on whether there is a velocity component v1from a vortex which delays the transmission, or a velocity component v2which hastens the transmission. As a result, receiver 34 will provide asignal which is frequency modulated by the passage of Karmans vortices.This signal is demodulated by the demodulator 36 whose output is used incounter or calculator 38 to provide a measure of fluid flow.

FIGS. 7 through 12 show alternate embodiments of the invention in whichthe element 14 is provided with passages extending between the recessesl6, 18 to communicate fluid fluctuations therebetween. Referring to FIG.7', the element 14 has a set of holes 40 extending between the recesses16, 18. The holes 40 are arranged in a straight line parallel tothe axisof the element 14, and are positioned adjacent the edges 20, 22 whereboundary layer separation occurs. As shown in FIG. 9, the fluid Fimpinging against the element 14 breaks into two streams F1 and F2, theboundary layers of which separate from the elements surface at the edges20, 22. When the vortices are shed from element 14, correspondingpressure fluctuations are produced next to the adjacent openings of theholes 40. Since the vortices are shed alternately from opposite sides ofthe element 14, the pressures within the recesses 16, 18 also willfluctuate in an alternating fashion. These pressure fluctuations causefluid to be displaced (i.e. to flow) through the holes 40 in analternating fashion, first in one direction and then a reverseddirection. The rate of pressure alternation is proportional to the rateof generation of vortices, and this in turn is proportional to the rateof fluid flow through the pipe. To detect fluid flowing through theholes 40, as shown in FIG. 9, a detecting means 12c may position anelectrically heated wire within the holes 40 to be responsive to thefluid flow without interfering with it.

. The holes 40 combine with recessed portions l6, 18 to improve thestable formation of Karmans vortices. Generally, when the boundary layerof a fluid flowing along the surface of an object is in a condition toseparate easily from the surface, flow of fluid outwardly against thelayer encourages its separation, and conversely, withdrawing fluid fromthe layer has the effect of retarding separation. Accordingly, theprovision of holes 40 adjacent the edges 20, 22 assists in controllingseparation of the boundary layer to thereby further improve thestability and reliability of vortex formation.

Referring to FIG. 8, an alternate embodiment of the invention is shown,in which a slot 40s, arranged parallel to the element axis, extendsbetween the recessed portions l6, 18 instead of the set of holes 40.

In FIGS. 10 and 11, an alternate embodiment is shown in which theelement 14 is formed on opposite sides thereof with respective sets ofholes 42 and 44. Each set of holes is arranged within a recess 16, 18ad- 5 jacent an edge 20, 22 in a straight line parallel to the axis ofthe cylinder and communicates with a corresponding interior cavity 46,48.

These cavities are separated by a central partition 50 having an opening52 serving as a passageway to accommodate the flow of fluidtherebetween. The interior cavities 46, 48, by equalizing pressure,provide a uniformity of flow distributed along the axis of element 14,and thus contribute to stable formation of Karmans vortices over theaxial distance L (FIG. 2) notwithstanding a variable velocitydistribution across the diameter of pipe 10. As shown in FIG. 10, thealternating flow of fluid through opening 52 can be detected by means12d positioning an electrically heated wire in the opening. Referring toFIG. 12, the rows of holes may be replaced by slots 42s and 44s, and thepartition opening may comprise a set of holes 52h arranged parallel tothe element axis.

In addition to the various detection means illustrated in FIGS. 1, 3, 9,and 10, the detection of fluid flow with elements having interiorcavitites 46, 48 may also be by detection means positioned in a chamberconnected to but remote from said cavitites, as disclosed in co-pendingapplication of H. Yamasaki et al., Ser. No. 108,731, tiled Jan. 22,1971.

Also, detection may be of the vortex interference pattern produced bytwo elements used in tandem, one upstream of the other, one or both ofthe elements being constructed according to FIGS. 2-12.

Although specific embodiments of the invention have been disclosedherein in detail, it is to be understood that this is for the purpose ofillustrating the invention, and should not be construed as necessarilylimiting the scope of the invention, since it is apparent that manychanges can be made to the disclosed structures by those skilled in theart to suit particular applications.

We claim:

1. A vortex generation element of the type used in flow meteringapparatus and having a generally elon-.

gate cylindrical shape placed transversely in a stream of fluid toproduce on opposite sides of the element vortices which are shed inalternating fashion, the flow metering apparatus having means formeasuring the frequency of vortex production to determine the velocityof the fluid stream, such element being characterized in that:

the element has formed on opposite sides thereof a recessed surfaceportion meeting the upstream surface of the element in an edge locatedat an angle, measured from the edge to the cylinder center to thecylinder stagnation point, lying within the range of angles at which theboundary layer of the fluid separates from the surface of an unrecessedcylindrical element at fluid velocities for which the rate of vortexproduction is substantially linearly related to fluid velocity; andmeeting the downstream surface of the element inwardly of said edge,whereby said edge forms an outer extremity of said element to said fluidflow.

2. An element as claimed in claim 1 wherein said edge is located at anangle of between approximately 70 and 105 measured from the edge to thecylinder center to the cylinder stagnation point.

3. An element as claimed in claim 2 wherein said angle is within therange of 75 to 85.

4. An element as claimed in claim 1 wherein said recessed surfaceportion is formed of at least one flat plane.

5. An element as claimed in claim 4 wherein said recessed portion isformed of two flat planes, the rear one of which is parallel to thedirection of fluid flow and the front one of which is perpendicular tothe direction of fluid flow.

6. An element as claimed in claim 1 wherein said recessed portion isformed of a curved surface.

7. An element as claimed in claim 1 wherein said cylinder is a rightcircular cylinder.

8. An element as claimed in claim 1 wherein said cylinder is anelliptical cylinder.

9. An element as claimed in claim 1 wherein said element furthercomprises means extending through said element between said recessedportions for communicating fluid fluctuations therebetween.

10. An element according to claim 9 wherein said communication meanscomprises a row of openings in said recessed portions arranged parallelto said element axis.

11. An element as claimed in claim 9 wherein said communicating meanscomprises a pair of interior cavities separated by a partition having apassageway therethrough, an opening means connecting said cavities withsaid recessed surface portions.

12. An element as claimed in claim 11 wherein said opening meanscomprises a row of holes.

13. An element as claimed in claim 11 wherein said opening meanscomprises a slot.

14. An element as claimed in claim 11 wherein said passageway comprisesa row of holes.

15. An element according to claim 11 wherein said measuring means ismounted in said passageway for detecting the fluid fluctuations therein.

16. An element as claimed in claim 9 wherein said measuring means ismounted in said communicating means for detecting the fluid fluctuationstherein.

17. An element as claimed in claim 1 wherein said measuring means ismounted on the downstream surface of said element for detecting fluidfluctuation therealong.

18. An element according to claim 1 wherein said measuring means islocated downstream of said element, said measuring means comprisingmeans transmitting a sound impulse transverse to the path of saidvortices, and means responsive to variations in the transmission timesof said impulses caused by the passage of said vortices.

1. A vortex generation element of the type used in flow meteringapparatus and having a generally elongate cylindrical shape placedtransversely in a stream of fluid to produce on opposite sides of theelement vortices which are shed in alternating fashion, the flowmetering apparatus having means for measuring the frequency of vortexproduction to determine the velocity of the fluid stream, such elementbeing characterized in that: the element has formed on opposite sidesthereof a recessed surface portion meeting the upstream surface of theelement in an edge located at an angle, measured from the edge to thecylinder center to the cylinder stagnation point, lying within the rangeof angles at which the boundary layer of the fluid separates from thesurface of an unrecessed cylindrical element at fluid velocities forwhich the rate of vortex production is substantially linearly related tofluid velocity; and meeting the downstream surface of the elementinwardly of said edge, whereby said edge forms an outer extremity ofsaid element to said fluid flow.
 2. An element as claimed in claim 1wherein said edge is located at an angle of between approximately 70*and 105* measured from the edge to the cylinder center to the cylinderstagnation point.
 3. An element as claimed in claim 2 wherein said angleis within the range of 75* to 85*.
 4. An element as claimed in claim 1wherein said recessed surface portion is formed of at least one flatplane.
 5. An element as claimed in claim 4 wherein said recessed portionis formed of two flat planes, the rear one of which is parallel to thedirection of fluid flow and the front one of which is perpendicular tothe direction of fluid flow.
 6. An element as claimed in claim 1 whereinsaid recessed portion is formed of a curved surface.
 7. An element asclaimed in claim 1 wherein said cylinder is a right circular cylinder.8. An element as claimed in claim 1 wherein said cylinder is anelliptical cylinder.
 9. An element as claimed in claim 1 wherein saidelement further comprises means extending through said element betweensaid recessed portions for communicating fluid fluctuationstherebetween.
 10. An element according to claim 9 wherein saidcommunication means comprises a row of openings in said recessedportions arranged parallel to said element axis.
 11. An element asclaimed in claim 9 wherein said communicating means comprises a pair ofinterior cavities separated by a partition having a passagewaytherethrough, an opening means connecting said cavities with saidrecessed surface portions.
 12. An element as claimed in claim 11 whereinsaid opening means comprises a row of holes.
 13. An element as claimedin claim 11 wherein said opening means comprises a slot.
 14. An elementas claimed in claim 11 wherein said passageway comprises a row of holes.15. An element according to claim 11 wherein said measuring means ismounted in said passageway for detecting the fluid fluctuations therein.16. An element as claimed in claim 9 wherein said measuring means ismounted in said communicating means for detecting the fluid fluctuationstherein.
 17. An element as claimed in claim 1 wherein said measuringmeans is mounted on the downstream surface of said element for detectingfluid fluctuation therealong.
 18. An element according to claim 1wherein said measuring means is located downstream of said element, saidmeasuring means comprising means transmitting a sound impulse transverseto the path of said vortices, and means responsive to variations in thetransmission times of said impulses caused by the passage of saidvortices.